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<Title>AdjacencyGraph</Title>
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<H2><A NAME="concept:AdjacencyGraph"></A>
AdjacencyGraph
</H2>

The AdjacencyGraph concept provides an interface for efficient access
of the adjacent vertices to a vertex in a graph. This is quite similar
to the <a href="./IncidenceGraph.html">IncidenceGraph</a> concept (the
target of an out-edge is an adjacent vertex). Both concepts are
provided because in some contexts there is only concern for the
vertices, whereas in other contexts the edges are also important.

<H3>Refinement of</H3>

<a href="Graph.html">Graph</a>

<h3>Notation</h3>

<Table>
<TR>
<TD><tt>G</tt></TD>
<TD>A type that is a model of Graph.</TD>
</TR>

<TR>
<TD><tt>g</tt></TD>
<TD>An object of type <tt>G</tt>.</TD>
</TR>

<TR>
<TD><tt>v</tt></TD>
<TD>An object of type <tt>boost::graph_traits&lt;G&gt;::vertex_descriptor</tt>.</TD>
</TR>

</table>


<H3>Associated Types</H3>

<Table border>

<tr>
<td><tt>boost::graph_traits&lt;G&gt;::traversal_category</tt><br><br>
 This tag type must be convertible to <tt>adjacency_graph_tag</tt>.
</td>
</tr>

<TR>
<TD><pre>boost::graph_traits&lt;G&gt;::adjacency_iterator</pre>
An adjacency iterator for a vertex <i>v</i> provides access to the
vertices adjacent to <i>v</i>.  As such, the value type of an
adjacency iterator is the vertex descriptor type of its graph. An
adjacency iterator must meet the requirements of <a
href="../../utility/MultiPassInputIterator.html">MultiPassInputIterator</a>.
</TD>
</TR>

</table>

<h3>Valid Expressions</h3>


<table border>

<tr>
<td><a name="sec:adjacent-vertices"><TT>adjacent_vertices(v,&nbsp;g)</TT></a></TD>
<TD>
Returns an iterator-range providing access to the vertices adjacent to
vertex <TT>v</TT> in graph <TT>g</TT>.<a
href="#1">[1]</a>

<br> Return type:
<TT>std::pair&lt;adjacency_iterator,&nbsp;adjacency_iterator&gt;</TT>
</TD>
</TR>

</table>

<H3>Complexity guarantees</H3>

The <TT>adjacent_vertices()</TT> function must return in constant time.

<H3>See Also</H3>

<a href="./graph_concepts.html">Graph concepts</a>,
<a href="./adjacency_iterator.html"><tt>adjacency_iterator</tt></a>

<H3>Concept Checking Class</H3>

<PRE>
  template &lt;class G&gt;
  struct AdjacencyGraphConcept
  {
    typedef typename boost::graph_traits&lt;G&gt;::adjacency_iterator
      adjacency_iterator;
    void constraints() {
      BOOST_CONCEPT_ASSERT(( MultiPassInputIteratorConcept&lt;adjacency_iterator&gt; ));

      p = adjacent_vertices(v, g);
      v = *p.first;
      const_constraints(g);
    }
    void const_constraints(const G&amp; g) {
      p = adjacent_vertices(v, g);
    }
    std::pair&lt;adjacency_iterator,adjacency_iterator&gt; p;
    typename boost::graph_traits&lt;G&gt;::vertex_descriptor v;
    G g;
  };
</PRE>

<h3>Design Rationale</h3>

The AdjacencyGraph concept is somewhat frivolous since <a
href="./IncidenceGraph.html">IncidenceGraph</a> really covers the same
functionality (and more).  The AdjacencyGraph concept exists because
there are situations when <tt>adjacent_vertices()</tt> is more
convenient to use than <tt>out_edges()</tt>. If you are constructing a
graph class and do not want to put in the extra work of creating an
adjacency iterator, have no fear. There is an adaptor class named <a
href="./adjacency_iterator.html"> <tt>adjacency_iterator</tt></a> that
you can use to create an adjacency iterator out of an out-edge
iterator.

<h3>Notes</h3>

<a name="1">[1]</a>  The case of a
<I>multigraph</I> (where multiple edges can connect the same two
vertices) brings up an issue as to whether the iterators returned by
the <TT>adjacent_vertices()</TT> function access a range that
includes each adjacent vertex once, or whether it should match the
behavior of the <TT>out_edges()</TT> function, and access a
range that may include an adjacent vertex more than once. For now the
behavior is defined to match that of <TT>out_edges()</TT>,
though this decision may need to be reviewed in light of more
experience with graph algorithm implementations.



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<TD nowrap>Copyright &copy; 2000-2001</TD><TD>
<A HREF="http://www.boost.org/people/jeremy_siek.htm">Jeremy Siek</A>, Indiana University (<A HREF="mailto:jsiek@osl.iu.edu">jsiek@osl.iu.edu</A>)
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